Introduction to Sports Biomechanics: Analysing Human Movement ...

The velocity can be obtained from the gradient – or slope – of a displacement–time
graph. Likewise acceleration can be obtained from the slope of a velocity–time
graph if we have one.
The acceleration can be obtained from the curvature of a displacement–time graph.
So, from our displacement–time graph, we can qualitatively describe two further
movement patterns; we can specify important features of the velocity–time pattern and
the acceleration–time pattern. As we will now see, this qualitative information will
answer fully the questions that our hypothetical sprint coach posed above.
The gradient – or slope – of a line should be intuitive. All you need to do is to
consider ‘walking’ along the graph from left to right:
If you are going uphill, the gradient, that is the velocity, is positive. This happens
throughout Figure 3.6.
If you are going downhill, the gradient and velocity are negative.
Where the direction changes from uphill to downhill, the gradient and velocity are
zero, and the gradient and velocity change from positive to negative.
Likewise, where the direction changes from downhill to uphill, the gradient and
velocity are zero and the gradient and velocity change from negative to positive.
This doesn’t, perhaps, seem to help much with our coach’s questions.
Curvature is probably less intuitive, so let us define two types of curvature as in
Figure 3.7, which we can call ‘valley-type’ and ‘hill-type’ curvature; we will also use the
terms ‘positive’ and ‘negative’ curvature. Positive curvature is what you would see
looking at a simple curved valley from the side and negative curvature corresponds
to the side view of a simple curved hill (Figure 3.7). Let us walk along the graph in
Figure 3.6 again, seeking this time to indicate curvature not gradient. At the start
of the race, the curvature is positive (valley-type); somewhere it changes at about 60%
of the race time to negative. And what is the gradient doing there? It changes from
becoming steeper to becoming less steep; in other words, the velocity stops increasing
and starts decreasing (Figure 3.8). Our coach’s novice performer takes 60% of the race
to reach maximum speed and then starts to slow down; we have answered our coach’s
question. This pattern is not, I must admit, typical for a good sprinter, who would
probably maintain a constant speed from about 30 m to 90 m, before slowing slightly,
Figure 3.7 Top: positive (valley-type) curvature; bottom: negative (hill-type) curvature.
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